When user preferences are locally coherent but globally diverse, the global model is insufficient to represent different local factors of the users. To address this problem, [1]} proposed the local low-rank assumption, where the global matrix may be in high rank but is a union of multiple low-rank sub-matrices composed of rows and columns with similar taste. It significantly relaxes the previous assumption that the matrix is globally at low-rank. Subsequent to the pioneering work, namely local low-rank matrix approximation (LLORMA) for rating prediction [1]}, [3]}, the local low-rank assumption was applied to follow-up works, either by allowing overlaps between local sub-matrices [4]}, [5]} or by splitting the entire matrix into disjoint multiple sub-matrices [6]}, [7]}.
